1. Field of Invention
This invention relates to devices used in fluid flow streams. Devices such as fluid distributor plates, filters, heat exchangers, valves, and flow metering plates.
2. Description of Prior Art
A variety of devices are used in fluid flow streams for filtering, controlling, exchanging heat, metering, and such. All such devices necessarily impede the flow to some extent. In forced flow streams such devices decrease pressure energy. Minimizing all such energy losses is desirable.
The invention herein described relates to the manufacture of plates that are perforated with two or more venturi orifices. The venturi orifices are to have "C.sub.d " discharge coefficient values that are greater than 1.0. "C.sub.d " is the discharge coefficient that is used in the flow formula for nozzles and orifices.
The flow formula referred to above and others are to be introduced hereinafter. Formulas are required to show that "C.sub.d " values greater than 1.0 have been implied by past patents that have been granted.
Textbooks on fluid flow present the following Bernoulli Equation for steady, frictionless, incompressible flow: EQU P.sub.1 /.rho..sub.1 +v.sub.1.sup.2 /2g+z.sub.1 =P.sub.2 /.rho..sub.2 +v.sub.2.sup.2 /2g+z.sub.2
where
P.sub.1 =initial pressure, lb per ft.sup.2 PA1 .rho..sub.1 =initial specific weight, lb per ft.sup.3 PA1 v.sub.1 =initial velocity, ft per sec PA1 g=32.2 ft per sec.sup.2 PA1 z.sub.1 =initial elevation with reference to some base elevation, ft
Any subsequent condition is P.sub.3, z.sub.3, etc.
All terms of the Bernoulli Equation result in feet of the fluid. The first term is called pressure head. The second term is called velocity head. The last term is called potential head.
Deriving formulas is simplified by making logical, practical, and acceptable assumptions. Assuming incompressible flow means that the specific weight does not change significantly over the range of conditions to be investigated. Thus, hereinafter, .rho..sub.1 =.rho..sub.2 =.rho..sub.3 =.rho.. Likewise, assume that the centerline of all flow streams are level. Thus, z.sub.1 =z.sub.2 =z.sub.3. So that the potential head terms will be dropped from the Bernoulli Equation used hereinafter.
Picture a still tank of some incompressible fluid with a perfect hole in its side at "h" feet below its surface. So that P.sub.1 =h.rho.. For the still tank v.sub.1 =0. Neglecting insignificant air pressure differences, P.sub.2 =0. Some of the fluid will emerge at a velocity of v.sub.2.
So that EQU P.sub.1 /.rho.=v.sub.2.sup.2 /2g=h.rho./.rho.=h
Resulting in EQU v.sub.2 =.sqroot.2gh
If the area of the theoretically perfect jet stream described above is A.sub.2, ft.sup.2, the rate of discharge is exactly: EQU Q=A.sub.2 v.sub.2, ft.sup.3 per sec
In this real world, the theoretically perfect is not possible. If a real nozzle were made in the tank wall as presumed above, the real discharge velocity would be in the range of 90% to 99% of the theoretical velocity. This introduces the concept of "C.sub.d " called the discharge coefficient. "C.sub.d " accounts for non-uniformity of velocity in the inlet and discharge, the rate of flow, fluid viscosity, and surface roughness. "C.sub.d " is preferably determined by actual measurement that is called calibration. So that the real rate of discharge is calculated by : EQU Q=C.sub.d A.sub.2 v.sub.2, ft.sup.3 per sec
Therefore, for nozzles discharging from a large space or plenum chamber, the value of "C.sub.d " is usually measured to be in the range of 0.90 to 0.99. Note that "C.sub.d " cannot be greater than 1.0 for nozzles.
If a circular sharp edged orifice is made in the tank wall presumed above, the real discharge rate is measured to be much lower than the theoretical rate. The primary reason for the much lower rate is that the fluid flow stream emerging from the sharp edged orifice contracts in cross sectional area. A coefficient of contraction is therefore measured to account for the reduction of the area of the orifice to that of the smallest area. This coefficient of contraction is usually measured to be in the range of 0.61 to 0.72. There is a further loss measured that is called the coefficient of velocity to account for friction losses that reduce the velocity in the smallest area from the theoretical velocity. The coefficient of velocity is usually measured to be in the range of 0.95 to 0.99. Thus, "C.sub.d " for circular sharp edged orifices is equal to the product of the coefficient of contraction and the coefficient of velocity. Note that "C.sub.d " cannot be greater than 1.0 for circular sharp edged orifices.
Nozzles, orifices, and venturi tubes are installed into mostly round pipe lines and ducts to measure flow rates. Now the entrance velocity may be of some significant value. The flow in equals the flow out, i.e., Q.sub.1 =Q.sub.2. So that: EQU Q.sub.1 =A.sub.1 v.sub.1 =A.sub.2 v.sub.2 =Q.sub.2
Back to the Bernoulli Equation, but this time v.sub.1 =A.sub.2 v.sub.2 /A.sub.1, and the outlet pressure P.sub.2 may now have some value.
So that EQU P.sub.1 /.rho.+(A.sub.2 v.sub.2 /A.sub.1).sup.2 /2g=P.sub.2 /.rho.+v.sub.2.sup.2 /2g
Resulting in EQU (P.sub.1 -P.sub.2)/.rho.=v.sub.2.sup.2 /2g1-(A.sub.2 /A.sub.1).sup.2 !
Now the real rate of discharge is calculated by: ##EQU1## Textbooks call the ratio of the throat diameter to the inlet diameter Beta. So that: EQU .beta.=d.sub.2 /d.sub.1 or .beta..sup.4 =(d.sub.2 /d.sub.1).sup.4 =(A.sub.2 /A.sub.1).sup.2
By substitution: ##EQU2##
Textbooks publish "C" flow coefficient values for orifices and nozzles where: ##EQU3##
"C" values for nozzles and orifices are reported above 1.0 when the value of Beta is large enough. "C" values are not to be confused with "C.sub.d " values. Nozzles, orifices, wire mesh screens, straight perforations, and such cannot have "C.sub.d " discharge coefficient values greater than 1.0.
The diverging discharge sections of venturi tubes that are designed for flow measurement with minimum pressure drop are made to restore the discharge pressure as nearly as possible to the inlet pressure. Some overall "C.sub.d " values can be calculated for such metering tubes that are marketed. See FIG. 4 of U.S. Pat. No. 4,174,734, to Bradham, (1979). Note that the ALLEN FLOW TUBE is shown as losing about 2.9% of the differential pressure at a Beta=0.75. Since no other data is given, it will be assumed here that the said flow tube had a "C.sub.d "=0.98 for the inlet to throat portion. The overall "C.sub.d " will be based upon the state measurement where (P.sub.1 -P.sub.3)=0.029 (P.sub.1 -P.sub.2), where P.sub.3 is the outlet pressure. The overall "C.sub.d " value will be based upon the throat area A.sub.2 since that is the standard for nozzles and orifices. Therefore: ##EQU4## Which reduces to EQU 0.98=C.sub.d .sqroot.0.029
Resulting in EQU C.sub.d =5.75
Likewise, from said FIG. 4, that for a LO-LOSS metering tube, that about 3.05% is the differential pressure loss at Beta=0.75.
This results in EQU 0.98=C.sub.d .sqroot.0.0305
So that EQU C.sub.d =5.61
Again, from said FIG. 4, that for a UNIVERSAL FLOW TUBE that about 3.45% is reported as the differential pressure loss at a Beta=0.75.
Thus EQU 0.98=C.sub.d .sqroot.0.0345
So EQU C.sub.d =5.28
Likewise, from said FIG. 4, that a VENTURI-LONG FORM is reported as having about 11.25% differential pressure loss at a Beta=0.75.
This results in EQU 0.98=C.sub.d .sqroot.0.1125
So that EQU C.sub.d =2.92
Lastly, from said FIG. 4, that a VENTURI-SHORT FORM is reported as having about 11.10% differential pressure loss at a Beta=0.75.
Now EQU 0.98=C.sub.d .sqroot.0.1110
So EQU C.sub.d =2.94